Forced oscillations (resonance)

The top of a spring pendulum (red circle) is moved to and fro - for example by hand; this motion is assumed as harmonic, which means that
it is possible to describe the motion by a cosine function. The oscillations of the spring pendulum caused in this way are called
forced oscillations.

The "Reset" button brings the spring pendulum to its initial position. You can start or stop and continue the simulation with the
other button. If you choose the option "Slow motion", the movement will be ten times slower. The spring constant, the mass,
the constant of attenuation and the angular frequency of the exciting oscillation can be changed within certain limits. In addition, you can
select one of three diagrams by using the appropriate radio buttons:

The elongations of exciter and resonator as functions of time

The amplitude of the resonator's oscillation dependent on the exciter's angular frequency

The phase difference between the oscillations of exciter and resonator dependent on the exciter's angular frequency

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On the whole you can see three different types of behaviour:

If the exciter's frequency is very small (this means that the top of the spring pendulum is moved very slowly), the pendulum will oscillate
nearly synchronously with the exciter and nearly with the same amplitude.

If the exciter's frequency agrees with the characteristic frequency of the spring pendulum, the oscillations of the pendulum will build up
more and more (resonance); in this case the oscillations are delayed about one fourth of the oscillation period
compared with the exciter.

If the exciter's frequency is very high, the resonator will oscillate only with a very small amplitude and nearly the opposite phase.

If the constant of attenuation (the friction) is very small, the transient states will be important too; therefore you have to wait some time
in this case to notice the mentioned types of behaviour.